#dft — Public Fediverse posts
Live and recent posts from across the Fediverse tagged #dft, aggregated by home.social.
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Won't be short of bedtime or bathtime reading this weekend.
DfT has published its latest Appraisal, Modelling and Evaluation Strategy, a set of research reports, and the 'live' TAG updates. There's a lot more than what's in the photo!
Plus the latest LTT out today.... and some interesting American research to catch up on if that's not enough...
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RAIL: Great Western Railway to be nationalised in December as south Wales services brought into public ownership
Great Western Railway (GWR), which runs services between London Paddington and south and south-west England and south Wales, will be nationalised on 13 December, the Department for Transport has announced.
It will become the eleventh operator to be brought into public ownership under the Government’s programme to reform the rail network, with the transfer forming part of the wider move towards a unified Great British Railways structure.
Three operators will remain in private hands after the change — Avanti West Coast, CrossCountry and East Midlands Railway, though CrossCountry is expected to follow into public ownership on 17 October next year.
A Department for Transport spokesperson said the move was “another significant moment” for the Government’s public ownership programme, adding that it brought “a simpler, more reliable network under Great British Railways a step closer.”
“The Government is delivering on its commitment to bring services back into public ownership and put passengers, not shareholders, at the heart of our railways,” the spokesperson added.
A Great British Railways train sporting the new Union Flag livery powers through the countryside — part of the UK Government’s rebranding of publicly owned rail services.The process does not involve the Government buying GWR outright. Instead, FirstGroup’s management contract is being allowed to expire, with the operation folding into a separate Government-owned entity known as DfT Operator — the same vehicle already used for LNER, Northern, Southeastern, TransPennine Express, South Western Railway and others.
GWR will be the twelfth company to join it once Govia Thameslink Railway transfers at the end of this month and Chiltern Railways follows in September. Great British Railways, which will ultimately replace the separate operator brands, is headquartered in Derby and expected to launch in 2027.
GWR said its priority throughout the transition would be “maintaining a punctual, reliable service for customers while continuing to support regional growth and connectivity across our network.” Transport Secretary Heidi Alexander has previously warned that renationalisation will not necessarily result in lower fares, with the focus instead on improving services and infrastructure.
The GWR nationalisation is the latest step in the creation of Great British Railways — though the Union Flag branding unveiled for the new national operator last December will not appear on local trains serving south-west Wales until later in the decade.
The announcement carries a particular twist for FirstGroup, which currently operates GWR and is set to lose the franchise to the state in December — while simultaneously building a new commercial foothold on the same Paddington corridor through its open access brand, Lumo.
A Lumo train on the East Coast Main Line. Lumo is operated by FirstGroup. Picture: LumoLumo has confirmed a December 2027 launch for a new direct Carmarthen to London Paddington service, calling at Llanelli, Gowerton, Cardiff, Newport, Severn Tunnel Junction and Bristol Parkway, running five return journeys a day using five new Hitachi trains on order.
Because Lumo operates as an open access operator rather than a franchised one, it falls outside the nationalisation programme — meaning FirstGroup stands to lose GWR to the state while retaining a commercial presence on the very same route through a different vehicle, effectively competing with a publicly-owned operator it previously ran itself.
The route has a long history. The original proposals were submitted by Grand Union Trains, which secured regulatory approval in 2022 following a battle with GWR, which had opposed the application. Grand Union subsequently sold its rights to the route to FirstGroup in 2024.
GWR cautioned that new services should not be detrimental to existing services or to future services already agreed, and said it would continue working with industry partners to develop services in the best interests of passengers and taxpayers. Carmarthenshire County Council had thrown its support behind the original Grand Union proposals, arguing a direct London connection would bring significant economic benefits to west Wales.
The Lumo service will give passengers at Carmarthen, Llanelli and Gowerton a genuine alternative to GWR on the London route for the first time — though it will not serve Milford Haven or Pembroke Dock directly.
Rail campaigners have also been pressing for funding clarity from the Welsh Government over a direct Milford Haven to London service, a commitment made by Welsh Labour ahead of this week’s Senedd election alongside a pledge of £50 million for Pembrokeshire rail upgrades. Transport for Wales is separately pursuing direct services between west Wales and Bristol Temple Meads, potentially serving Milford Haven, Swansea, Neath, Carmarthen and Bridgend from September 2026.
The broader question of what public ownership means for the region’s longer-term rail ambitions — including the £14 billion metro vision for Swansea and west Wales — remains to be seen as Great British Railways takes shape.
Our rail coverage
Lumo to launch direct Carmarthen to London Paddington service in December 2027 — with stops at Llanelli and Gowerton
The full story of how the route went from Grand Union proposal to FirstGroup reality.Transport for Wales wants to run trains to Bristol — and it could mean direct services from Milford Haven, Swansea and Carmarthen
New direct services to Bristol could transform connectivity across west Wales.Campaigners demand funding answers as Labour pledges direct Milford Haven to London train service
Rail campaigners question where the money will come from for Wales’s £14 billion rail pipeline.Union flag rail designs unveiled — South West Wales impact comes later
What Great British Railways branding means for trains in our region.£14bn metro dream for Swansea — but will West Wales finally get its share?
#DepartmentForTransport #DfT #featured #GreatBritishRailways #GreatWesternRailway #LondonPaddington #Lumo #nationalisation #rail #renationalisation
The long-term vision for rail investment across the region. -
Spent some time recently tracing the history of the discount rate guidance in various recent editions of the Green Book and its supplementary documents.
The guidance has changed, and in the latest Forthcoming Change notices from DfT, TAG is now taking more of it on board.
It’s a complicated story. The kitchen table came in handy…
Look out for the resulting thoughts, in this week’s edition of Local Transport Today.
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Birmingham-Manchester railway won’t be developed until HS2 and NPR completed
The Department for Transport (DfT) has stated the delivery of proposals to connect Birmingham and Manchester with a…
#Birmingham #UnitedKingdom #UK #GB #England #Headlines #News #Europe #EU #Britain #DfT #GreatBritain #HS2 #HS2Phase2 #nista #northernpowerhouserail #NPR #public-accounts-committee
https://www.europesays.com/uk/911803/ -
https://www.europesays.com/uk/911803/ Birmingham-Manchester railway won’t be developed until HS2 and NPR completed #Birmingham #Britain #DfT #England #GreatBritain #HS2 #HS2Phase2 #nista #NorthernPowerhouseRail #NPR #PublicAccountsCommittee #UK #UnitedKingdom
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🇮🇹 Just back from an intensive Erasmus+ Staff Mobility at the Università della Calabria in Cosenza, Italy.
Incredible opportunity to reunite with Prof. Nino Russo – nearly 5 years after my PhD student visit in 2021!
The results? We’ve already outlined four new joint research papers that will launch soon. Major step forward in our Polish-Italian scientific collaboration. 🚀
#ErasmusPlus #StaffMobility #UniCal #ComputationalChemistry #DFT #PDT #WroclawMedicalUniversity
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Зачем нужен Design for Testability (DFT) и как его реализуют в FPGA
Привет, Хабр! Меня зовут Антон Осетров, я разрабатываю СнК в компании
https://habr.com/ru/companies/yadro/articles/1006004/
#dft #design_for_manufacturing #rtl #fpga #fpga+soc #verilog #testing #испытания #design_for_testability #atpg
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Зачем нужен Design for Testability (DFT) и как его реализуют в FPGA
Привет, Хабр! Меня зовут Антон Осетров, я разрабатываю СнК в компании
https://habr.com/ru/companies/yadro/articles/1006004/
#dft #design_for_manufacturing #rtl #fpga #fpga+soc #verilog #testing #испытания #design_for_testability #atpg
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Зачем нужен Design for Testability (DFT) и как его реализуют в FPGA
Привет, Хабр! Меня зовут Антон Осетров, я разрабатываю СнК в компании
https://habr.com/ru/companies/yadro/articles/1006004/
#dft #design_for_manufacturing #rtl #fpga #fpga+soc #verilog #testing #испытания #design_for_testability #atpg
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Зачем нужен Design for Testability (DFT) и как его реализуют в FPGA
Привет, Хабр! Меня зовут Антон Осетров, я разрабатываю СнК в компании
https://habr.com/ru/companies/yadro/articles/1006004/
#dft #design_for_manufacturing #rtl #fpga #fpga+soc #verilog #testing #испытания #design_for_testability #atpg
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(1/2)
I found a nice improvement to the Constant-Q Sliding DFT¹.Using single precision calculation (32-bit float) generates some remanent noise because of the recursive nature of the algorithm: a running sum combined with complex rotations.
Replacing the complex multiply in eq. 3 for the twiddle factors (outer exponential) with the Martin Vicanek’s quadrature oscillator² helps a lot in the low frequencies. About 30 dB of improvement here, almost no extra CPU cost.
¹ A transform turning a PCM signal into a frequency spectrum. https://www.dafx.de/paper-archive/details.php?id=QMFQa1rIAM7mwu9tMIZAlg
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ML против ядерных отходов. Как мы ускорили вычисление свойств карбидов технеция с помощью нейросетей
Привет Хабр! Меня зовут Радион Зарипов, я — аспирант программы «Науки о материалах» в Сколтехе и прохожу в настоящее время стажировку в Sber AI. Значительная часть работы, о которой пойдет речь, была выполнена мной во время летней практики в AIRI, в группе «Дизайн новых материалов», которая исследует возможности применения вычислительных подходов к прогнозированию новых материалов. Совместно с моими коллегами из Сколтеха, AIRI, Sber AI, РХТУ и ИФХЭ РАН мы недавно опубликовали статью в Acta Materialia , где построили подробную фазовую диаграмму карбида технеция. Это не было бы возможным без применения графовых нейронных сетей, которые заменяют существенную часть вычислений. Здесь мне хотелось бы подробнее рассказать, что именно мы делали и с какими сложностями столкнулись. Текст получился большим и подробным, но если вам интересно, как машинное обучение постепенно меняет материаловедение, эта статья для вас.
https://habr.com/ru/companies/airi/articles/994806/
#Ядерные_отходы #Карбиды_технеция #Фазовая_диаграмма #DFT #ML #GNN
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Our work is also described in a scientific highlight from the NCCR Marvel collaboration: https://nccr-marvel.ch/highlights/AD-DFPT-Herbst
#dftk #algorithmicdifferentiation #densityfunctionaltheory #dft
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Our work is also described in a scientific highlight from the NCCR Marvel collaboration: https://nccr-marvel.ch/highlights/AD-DFPT-Herbst
#dftk #algorithmicdifferentiation #densityfunctionaltheory #dft
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Our work is also described in a scientific highlight from the NCCR Marvel collaboration: https://nccr-marvel.ch/highlights/AD-DFPT-Herbst
#dftk #algorithmicdifferentiation #densityfunctionaltheory #dft
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New publication https://doi.org/10.1038/s41524-025-01880-3
Our work on AD-DFPT, a unification of #automaticdifferentiation with linear response for #densityfunctionaltheory is published in npj Computational Materials. We show examples for #property predition, #uncertainty propagation, the design of #materials and #machinelearning of new #dft models. #condensedmatter #dftk -
New publication https://doi.org/10.1038/s41524-025-01880-3
Our work on AD-DFPT, a unification of #automaticdifferentiation with linear response for #densityfunctionaltheory is published in npj Computational Materials. We show examples for #property predition, #uncertainty propagation, the design of #materials and #machinelearning of new #dft models. #condensedmatter #dftk -
New publication https://doi.org/10.1038/s41524-025-01880-3
Our work on AD-DFPT, a unification of #automaticdifferentiation with linear response for #densityfunctionaltheory is published in npj Computational Materials. We show examples for #property predition, #uncertainty propagation, the design of #materials and #machinelearning of new #dft models. #condensedmatter #dftk -
[Перевод] Fizz Buzz на косинусах
Fizz Buzz — это игра с числами, которая стала неожиданно популярной в мире компьютерного программирования в качестве простой проверки базовых навыков. Правила игры просты: игроки вслух произносят по порядку числа, начиная с единицы. Если число делится на 3, игрок должен сказать вместо него «Fizz». Если число делится на 5, он должен сказать «Buzz». Если оно делится и на 3, и на 5, игрок говорит «FizzBuzz». Вот типичная программа на Python, выводящая нужную последовательность: for n in range(1, 101): if n % 15 == 0: print('FizzBuzz') elif n % 3 == 0: print('Fizz') elif n % 5 == 0: print('Buzz') else: print(n) А вот её вывод: fizz-buzz.txt . Можно ли усложнить эту программу? Слова «Fizz», «Buzz» и «FizzBuzz» повторяются в этой последовательности периодически. А что ещё у нас есть периодического? Тригонометрические функции! Возможно, нам удастся при помощи этих функций закодировать все четыре правила последовательности в выражении в аналитическом виде. Именно эту задачу мы и исследуем в статье, получив в конце дискретный ряд Фурье, который может получить любое целочисленное n и выбрать для печати соответствующий текст.
https://habr.com/ru/articles/969856/
#косинус #тригонометрические_функции #дискретное_преобразование_фурье #dft
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Stopped by Target today and the only #magicthegathering product they had on the shelves was Aetherdrift and Spider-Man. Usually they don’t have anything which suggests to me that those sets are indeed clunkers. #mtg #dft #spm
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New preprint https://arxiv.org/abs/2511.06957
A #perspective discussing Moreau-Yosida (MY) techniques in #densityfunctionaltheory.
MY regularisation has enabled to import tools from #convexanalysis into #dft
providing a new mathematical understanding of the most important atomistic simulation approach
and new robust algorithms for Kohn-Sham #dft.Thanks to my co-authors from the #hylleraas centre and #oslomet for insightful discussions.
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New preprint https://arxiv.org/abs/2511.06957
A #perspective discussing Moreau-Yosida (MY) techniques in #densityfunctionaltheory.
MY regularisation has enabled to import tools from #convexanalysis into #dft
providing a new mathematical understanding of the most important atomistic simulation approach
and new robust algorithms for Kohn-Sham #dft.Thanks to my co-authors from the #hylleraas centre and #oslomet for insightful discussions.
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Lots of technical updates on transport modelling and #appraisal coming out of #DfT recently.
My application to host #Strictly might have to wait until I've read all these and responded to the mini-consultation on road freight values of time...
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This report👇 is worth reading - but I'm biased! Delighted to have been part of the team producing it for the Transport Planning Society.
If you want to know what the Treasury's 2025 Green Book Review really means for transport business cases, this report is for you.
We also have recommendations on how transport appraisal in England should evolve in response to the review - and indeed to better reflect Green Book principles. Many are for #DfT who produce #TAG and other guidance for England. But the issues and ideas will be of interest to sub-national transport bodies and local government too.
We also have some mythbusting!
And some suggestions for what practitioners can do on their own projects, to help decision-makers make better decisions and deliver the right things.
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Another set of bereaved parents in #England calling for graduated #driving #licences - but (for once) I agree with the #DfT and Government!
Realistically its not feasible to implement - how would they even be enforced? Old bill would have to pull over every car with young people inside and check their ages, there aren't even enough officers around to do that and if there were, they would be better deployed enforcing existing traffic laws.
In any case the real reasons behind many of these collisions are #ToxicMasculinity and #LadCulture - which is by no means confined to 17 year olds, and is very often enabled by their fathers (something I've unearthed myself after monitoring social media profiles of young people involved in RTCs )
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Another set of bereaved parents in #England calling for graduated #driving #licences - but (for once) I agree with the #DfT and Government!
Realistically its not feasible to implement - how would they even be enforced? Old bill would have to pull over every car with young people inside and check their ages, there aren't even enough officers around to do that and if there were, they would be better deployed enforcing existing traffic laws.
In any case the real reasons behind many of these collisions are #ToxicMasculinity and #LadCulture - which is by no means confined to 17 year olds, and is very often enabled by their fathers (something I've unearthed myself after monitoring social media profiles of young people involved in RTCs )
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Another set of bereaved parents in #England calling for graduated #driving #licences - but (for once) I agree with the #DfT and Government!
Realistically its not feasible to implement - how would they even be enforced? Old bill would have to pull over every car with young people inside and check their ages, there aren't even enough officers around to do that and if there were, they would be better deployed enforcing existing traffic laws.
In any case the real reasons behind many of these collisions are #ToxicMasculinity and #LadCulture - which is by no means confined to 17 year olds, and is very often enabled by their fathers (something I've unearthed myself after monitoring social media profiles of young people involved in RTCs )
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Another set of bereaved parents in #England calling for graduated #driving #licences - but (for once) I agree with the #DfT and Government!
Realistically its not feasible to implement - how would they even be enforced? Old bill would have to pull over every car with young people inside and check their ages, there aren't even enough officers around to do that and if there were, they would be better deployed enforcing existing traffic laws.
In any case the real reasons behind many of these collisions are #ToxicMasculinity and #LadCulture - which is by no means confined to 17 year olds, and is very often enabled by their fathers (something I've unearthed myself after monitoring social media profiles of young people involved in RTCs )
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Another set of bereaved parents in #England calling for graduated #driving #licences - but (for once) I agree with the #DfT and Government!
Realistically its not feasible to implement - how would they even be enforced? Old bill would have to pull over every car with young people inside and check their ages, there aren't even enough officers around to do that and if there were, they would be better deployed enforcing existing traffic laws.
In any case the real reasons behind many of these collisions are #ToxicMasculinity and #LadCulture - which is by no means confined to 17 year olds, and is very often enabled by their fathers (something I've unearthed myself after monitoring social media profiles of young people involved in RTCs )
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New resource: An at-a-glance summary of the government’s transport objectives in England.
DfT recently updated its list of priorities – with little fanfare. This handy one-page guide sets them out, alongside the wider government objectives and the main linkages between the two levels.
Ideal for those tricky 'policy review' texts…
On my website at https://grahamjames.co.uk/transport-policy/
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New preprint: https://arxiv.org/abs/2509.07785
We present an implementation of AD-DFPT, a unification of #automaticdifferentiation with classical #dfpt response techniques for #densityfunctionaltheory (#dft). We demonstrate its use for #property predition, #uncertainty propagation, design of new #materials as well as the #machinelearning of new #dft models.
#condensedmatter #planewave #response #physics #simulation #computation
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UK Ports: Fossil fuels dusk while electricity is dawning http://dlvr.it/TMkZPG #DepartmentforTransport #DFT #Environment #NatPowerMarine
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UK Ports: Fossil fuels dusk while electricity is dawning http://dlvr.it/TMkZPG #DepartmentforTransport #DFT #Environment #NatPowerMarine
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UK Ports: Fossil fuels dusk while electricity is dawning http://dlvr.it/TMkZPG #DepartmentforTransport #DFT #Environment #NatPowerMarine
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UK Ports: Fossil fuels dusk while electricity is dawning http://dlvr.it/TMkZPG #DepartmentforTransport #DFT #Environment #NatPowerMarine
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UK Ports: Fossil fuels dusk while electricity is dawning http://dlvr.it/TMkZPG #DepartmentforTransport #DFT #Environment #NatPowerMarine
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От месяцев к минутам. Как мы применяем машинное обучение для поиска перспективных литий-ионных проводников
Привет, я Артем Дембицкий, аспирант программы «Науки о материалах» и стажёр‑исследователь Центра энергетических технологий Сколтеха, а также младший научный сотрудник команды «Дизайн новых материалов» Института AIRI. Мы с коллегами используем модели машинного обучения для разработки новых материалов с улучшенными свойствами. Недавно статья с результатами нашего исследования вышла в npj Computational materials — журнале из семейства Nature. Совместными усилиями Сколтеха и AIRI мы оценили применимость машинного обучения для ускоренного поиска литий‑ионных проводников, а также показали практический пример использования универсальных межатомных потенциалов для подбора защитных покрытий катодов твердотельных аккумуляторов. В этой статье хотелось поделиться подробностями нашей работы, а также в целом рассказать об этих материалах и о том, как их ищут.
https://habr.com/ru/companies/airi/articles/917194/
#MLforchemistry #литийионные_аккумуляторы #dft #MLIP #uMLIP #литийионные_проводники
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От месяцев к минутам. Как мы применяем машинное обучение для поиска перспективных литий-ионных проводников
Привет, я Артем Дембицкий, аспирант программы «Науки о материалах» и стажёр‑исследователь Центра энергетических технологий Сколтеха, а также младший научный сотрудник команды «Дизайн новых материалов» Института AIRI. Мы с коллегами используем модели машинного обучения для разработки новых материалов с улучшенными свойствами. Недавно статья с результатами нашего исследования вышла в npj Computational materials — журнале из семейства Nature. Совместными усилиями Сколтеха и AIRI мы оценили применимость машинного обучения для ускоренного поиска литий‑ионных проводников, а также показали практический пример использования универсальных межатомных потенциалов для подбора защитных покрытий катодов твердотельных аккумуляторов. В этой статье хотелось поделиться подробностями нашей работы, а также в целом рассказать об этих материалах и о том, как их ищут.
https://habr.com/ru/companies/airi/articles/917194/
#MLforchemistry #литийионные_аккумуляторы #dft #MLIP #uMLIP #литийионные_проводники
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От месяцев к минутам. Как мы применяем машинное обучение для поиска перспективных литий-ионных проводников
Привет, я Артем Дембицкий, аспирант программы «Науки о материалах» и стажёр‑исследователь Центра энергетических технологий Сколтеха, а также младший научный сотрудник команды «Дизайн новых материалов» Института AIRI. Мы с коллегами используем модели машинного обучения для разработки новых материалов с улучшенными свойствами. Недавно статья с результатами нашего исследования вышла в npj Computational materials — журнале из семейства Nature. Совместными усилиями Сколтеха и AIRI мы оценили применимость машинного обучения для ускоренного поиска литий‑ионных проводников, а также показали практический пример использования универсальных межатомных потенциалов для подбора защитных покрытий катодов твердотельных аккумуляторов. В этой статье хотелось поделиться подробностями нашей работы, а также в целом рассказать об этих материалах и о том, как их ищут.
https://habr.com/ru/companies/airi/articles/917194/
#MLforchemistry #литийионные_аккумуляторы #dft #MLIP #uMLIP #литийионные_проводники
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От месяцев к минутам. Как мы применяем машинное обучение для поиска перспективных литий-ионных проводников
Привет, я Артем Дембицкий, аспирант программы «Науки о материалах» и стажёр‑исследователь Центра энергетических технологий Сколтеха, а также младший научный сотрудник команды «Дизайн новых материалов» Института AIRI. Мы с коллегами используем модели машинного обучения для разработки новых материалов с улучшенными свойствами. Недавно статья с результатами нашего исследования вышла в npj Computational materials — журнале из семейства Nature. Совместными усилиями Сколтеха и AIRI мы оценили применимость машинного обучения для ускоренного поиска литий‑ионных проводников, а также показали практический пример использования универсальных межатомных потенциалов для подбора защитных покрытий катодов твердотельных аккумуляторов. В этой статье хотелось поделиться подробностями нашей работы, а также в целом рассказать об этих материалах и о том, как их ищут.
https://habr.com/ru/companies/airi/articles/917194/
#MLforchemistry #литийионные_аккумуляторы #dft #MLIP #uMLIP #литийионные_проводники
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New publication https://doi.org/10.1103/PhysRevB.111.205143
New algorithm for the #inverseproblem of Kohn-Sham #densityfunctionaltheory (#dft), i.e. to find the #potential from the #density.
Outcome of a fun collaboration of @herbst with the group of Andre Laestadius at #oslomet to derive first mathematical error bounds for this problem
#condensedmatter #planewave #numericalanalysis #convexanalysis #dftk
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New publication https://doi.org/10.1103/PhysRevB.111.205143
New algorithm for the #inverseproblem of Kohn-Sham #densityfunctionaltheory (#dft), i.e. to find the #potential from the #density.
Outcome of a fun collaboration of @herbst with the group of Andre Laestadius at #oslomet to derive first mathematical error bounds for this problem
#condensedmatter #planewave #numericalanalysis #convexanalysis #dftk
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https://www.europesays.com/uk/130347/ Renationalisation of Britain’s train services begins #Britain #BritishRailways #DfT #England #GreatBritain #HeidiAlexander #LondonWaterloo #NorthernIreland #PublicControl #PublicOwnership #RailServices #Scotland #SouthWesternRailway #SWR #TheGovernment #UK #UnitedKingdom #Wales
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New preprint from our team: https://arxiv.org/abs/2409.04372
A new algorithm for computing #material properties in #densityfunctionaltheory (#dft) based on inexact #krylov methods: we safe 40% computational cost by an adaptive selection of convergence tolerances inspired from #mathematical analysis.
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The Fourier Transform is a mathematical operation that transforms a function of time (or space) into a function of frequency. It decomposes a complex signal into its constituent sinusoidal components, each with a specific frequency, amplitude, and phase. This is particularly useful in many fields, such as signal processing, physics, and engineering, because it allows for analysing the frequency characteristics of signals. The Fourier Transform provides a bridge between the time and frequency domains, enabling the analysis and manipulation of signals in more intuitive and computationally efficient ways. The result of applying a Fourier Transform is often represented as a spectrum, showing how much of each frequency is present in the original signal.
\[\Large\boxed{\boxed{\widehat{f}(\xi) = \int_{-\infty}^{\infty} f(x)\ e^{-i 2\pi \xi x}\,\mathrm dx, \quad \forall\xi \in \mathbb{R}.}}\]
Inverse Fourier Transform:
\[\Large\boxed{\boxed{ f(x) = \int_{-\infty}^{\infty} \widehat f(\xi)\ e^{i 2 \pi \xi x}\,\mathrm d\xi,\quad \forall x \in \mathbb R.}}\]The equation allows us to listen to mp3s today. Digital Music Couldn’t Exist Without the Fourier Transform: http://bit.ly/22kbNfi
#Fourier #FourierTransform #Transform #Time #Frequency #Space #TimeDomain #FrequencyDomain #Wavenumber #WavenumberDomain #Function #Math #Maths #JosephFourier #Signal #Signals #FT #IFT #DFT #FFT #Physics #SignalProcessing #Engineering #Analysis #Computing #Computation #Operation #ComplexSignal #Sinusoidal #Amplitude #Phase #Spectra #Spectrum #Pustam #Raut #PustamRaut #EGR #Mathstodon #Mastodon #GeoFlow #SpectralMethod
